Question: Is ${420126}$ divisible by $4$ ?
Answer: A number is divisible by $4$ if the last two digits are divisible by $4$ . [ Why? We can rewrite the number as a multiple of $100$ plus the last two digits: $ \gray{4201} {26} = \gray{4201} \gray{00} + {26} $ Because $420100$ is a multiple of $100$ , it is also a multiple of $4$ So as long as the value of the last two digits, ${26}$ , is divisible by $4$ , the original number must also be divisible by $4$ Is the value of the last two digits, $26$ , divisible by $4$ No, $26$ is not divisible by $4$, so $420126$ is also not divisible by $4$.